Question 24026: If Kelly bought 3 pens and 4 pencils that cost 7.42 and Bill bought 4 pens and 5 pencils that cost 9.62 what is the cost of one pen and one pencil
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! Let x = cost of 1 pen
y = cost of 1 pencil
3x+4y = 7.42
4x+5y = 9.62
You have two equations and two variables, and I think the easiest way to solve this is to eliminate either the x or y coefficients. The x coefficients are smaller, so find the common multiple of 3 and 4. In other words, what number can you find that both 3 and 4 divide evenly into? Answer is 12. To get a 12 for the first equation, multiply both sides of the first equation by 4, and the second equation by 3. Also, multiply both sides of the second equation by -1, to make it a +12x and a -12x, which will subtract out:
3x+4y = 7.42
4x+5y = 9.62
4*(3x+4y) = 4*(7.42)
-3*(4x+5y) = -3*(9.62)
12x + 16y = 29.68
-12x - 15y = -28.86
Add these two equations together, and the x terms subtract out:
1y = .82
y = $.82
Now, go back to the first equation and substitute this value for y:
3x+4*.82 = 7.42
3x + 3.28 = 7.42
3x +3.28 = 7.42- 3.28
3x = 4.14
Divide both sides by 3:
x= $1.38
Check this answer by substituting both values in the second equation:
4x+5y = 9.62
4*1.38+5*.82 = 9.62
$5.52 + 4.10 = 9.62
It checks!
R^2 at SCC
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